The exhaust line comprises an injection segment including at least one cup having a large upstream face directly sprayed with the exhaust gases and dividing a circulation passage into an upstream space and a downstream space. The injection segment comprises at least one circumferential conduit fluidically connecting the upstream space to the downstream space. The cup defines at least one injection channel and at least one guiding area laid out so as to guide as far as said injection channel a portion of the exhaust gases spraying the large upstream face. An injection device includes a reagent injector that is oriented to inject the reagent substantially with a co-current or counter-current of the exhaust gases in the injection channel, with the latter extending from the injector as far as the inlet of the conduit.